Two trains are moving at 30 m/s in opposite directions on the same track. the engineers see simultaneously that they are on a collision course and apply the brakes when they are 1000 m apart. assuming both trains have the same acceleration, what must this acceleration be if the trains are to stop just short of colliding?

Acceleration of train needed to avoid collision = -0.9 m/s²

Explanation:

Here both trains are similar with 1000 m apart with same speed.

So one train has to move 500 m before stopping just to avoid collision.

We have

Initial velocity, u =  30 m/s

Acceleration , a = ?

Displacement, s = 500 m

Final velocity, v = 0 m/s

We have equation of motion v²= u² + 2as

Substituting

     v²= u² + 2as

     0²= 30² + 2 x a x 500

    a = -0.9 m/s²

Acceleration of train needed to avoid collision = -0.9 m/s²

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